Symmetry of tilings of the plane

Radin, Charles

doi:10.1090/S0273-0979-1993-00425-7

Symmetry of tilings of the plane
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Bull. Amer. Math. Soc. 29 (1993), 213-217 Request permission

Abstract:

We discuss two new results on tilings of the plane. In the first, we give sufficient conditions for the tilings associated with an inflation rule to be uniquely ergodic under translations, the conditions holding for the pinwheel inflation rule. In the second result we prove there are matching rules for the pinwheel inflation rule, making the system the first known to have complete rotational symmetry.

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